Variance reduction properties of the reparameterization trick

By Ming Xu, Matias Quiroz, Robert Kohn, Scott Anthony Sisson. 2018

83 citations recorded by the source corpus.

The reparameterization trick is widely used in variational inference as it yields more accurate estimates of the gradient of the variational objective than alternative approaches such as the score function method. Although there is overwhelming empirical evidence in the literature showing its success, there is relatively little research exploring why the reparameterization trick is so effective. We explore this under the idealized assumptions that the variational approximation is a mean-field Gaussian density and that the log of the joint density of the model parameters and the data is a quadratic function that depends on the variational mean. From this, we show that the marginal variances of the reparameterization gradient estimator are smaller than those of the score function gradient estimator. We apply the result of our idealized analysis to real-world examples.

Subfields: Artificial Intelligence, Molecular Biology, Statistics and Probability

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Citations in the corpus

Monte Carlo Gradient Estimation in Machine Learning (2019, background): “Since most of the functions we will work with will not be Lipschitz continuous, Xu et al. (2018) use a different set of simplifying assumptions to develop an understanding of the variance that reinforces the general intuition built here.”
Stochastic Normalizing Flows (2020, result): “The reduction of a random ODE to this form is in keeping with the reparameterization trick (Xu et al., 2019).”